Addendum to the paper: Compact embedded minimal surfaces in the Berger sphere

Heayong Shin; Young Wook Kim; Sung-Eun Koh; Hyung Yong Lee; Seong-Deog Yang

doi:10.5802/crmath.403

Géométrie et Topologie

Addendum to the paper: Compact embedded minimal surfaces in the Berger sphere
[Addendum à l’article : Surfaces minimales compactes intégrées dans la sphère Berger]

Heayong Shin ¹ ; Young Wook Kim ² ; Sung-Eun Koh ³ ; Hyung Yong Lee ² ; Seong-Deog Yang ²

¹ Department of Mathematics, Chung-Ang University, Seoul 06974, Korea
² Department of Mathematics, Korea University, Seoul 02841, Korea
³ Department of Mathematics, Konkuk University, Seoul 05029, Korea

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 257-264.

complète Compact embedded minimal surfaces in the Berger sphere
[Surfaces minimales compactes intégrées dans la sphère de Berger]

Résumé
Abstract

Nous construisons une famille à deux paramètres discrets de surfaces minimales compactes plongées dans la sphère de Berger qui peut être considérée comme l’analogue de l’hélicoïde de Karcher-Scherk.

We construct a two discrete parameter family of compact minimal surfaces embedded in the Berger sphere which may be considered as the analogue of the helicoidal Karcher-Scherk surfaces.

Reçu le : 2021-04-09
Révisé le : 2022-02-16
Accepté le : 2022-06-29
Publié le : 2023-01-12

DOI : 10.5802/crmath.403

Affiliations des auteurs :

Heayong Shin ¹ ; Young Wook Kim ² ; Sung-Eun Koh ³ ; Hyung Yong Lee ² ; Seong-Deog Yang ²

¹ Department of Mathematics, Chung-Ang University, Seoul 06974, Korea
² Department of Mathematics, Korea University, Seoul 02841, Korea
³ Department of Mathematics, Konkuk University, Seoul 05029, Korea

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2023__361_G1_257_0,
     author = {Heayong Shin and Young Wook Kim and Sung-Eun Koh and Hyung Yong Lee and Seong-Deog Yang},
     title = {Addendum to the paper: {Compact} embedded minimal surfaces in the {Berger} sphere},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {257--264},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.403},
     language = {en},
}

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Heayong Shin; Young Wook Kim; Sung-Eun Koh; Hyung Yong Lee; Seong-Deog Yang. Addendum to the paper: Compact embedded minimal surfaces in the Berger sphere. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 257-264. doi : 10.5802/crmath.403. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.403/

Bibliographie
Cité par

[1] (https://minimalsurfaces.blog/home/repository/singly-periodic/ helicoidal-karcher-scherk-surfaces/)

[2] III Meeks; Shing-Tung Yau The existence of embedded minimal surfaces and the problem of uniqueness, Math. Z., Volume 179 (1982), pp. 151-168 | DOI | MR | Zbl

[3] Heayong Shin; Young Wook Kim; Sung-Eun Koh; Hyung Yong Lee; Seong-Deog Yang Ruled minimal surfaces in the Berger sphere, Differ. Geom. Appl., Volume 40 (2015), pp. 209-222 | DOI | MR | Zbl

[4] Heayong Shin; Young Wook Kim; Sung-Eun Koh; Hyung Yong Lee; Seong-Deog Yang Compact embedded minimal surfaces in the Berger sphere, C. R. Acad. Sci. Paris, Volume 356 (2018) no. 3, pp. 333-339 | DOI | MR | Zbl

[5] Heayong Shin; Young Wook Kim; Sung-Eun Koh; Hyung Yong Lee; Seong-Deog Yang Schwarz’ CLP-surfaces in ${Nil}_{3}$ , Proc. Am. Math. Soc., Volume 147 (2019) no. 4, pp. 1677-1685 | DOI | Zbl

[6] Francisco Torralbo Compact minimal surfaces in the Berger spheres, Ann. Global Anal. Geom., Volume 41 (2012) no. 4, pp. 391-405 | DOI | MR | Zbl

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